12,186 research outputs found
Oblivious Bounds on the Probability of Boolean Functions
This paper develops upper and lower bounds for the probability of Boolean
functions by treating multiple occurrences of variables as independent and
assigning them new individual probabilities. We call this approach dissociation
and give an exact characterization of optimal oblivious bounds, i.e. when the
new probabilities are chosen independent of the probabilities of all other
variables. Our motivation comes from the weighted model counting problem (or,
equivalently, the problem of computing the probability of a Boolean function),
which is #P-hard in general. By performing several dissociations, one can
transform a Boolean formula whose probability is difficult to compute, into one
whose probability is easy to compute, and which is guaranteed to provide an
upper or lower bound on the probability of the original formula by choosing
appropriate probabilities for the dissociated variables. Our new bounds shed
light on the connection between previous relaxation-based and model-based
approximations and unify them as concrete choices in a larger design space. We
also show how our theory allows a standard relational database management
system (DBMS) to both upper and lower bound hard probabilistic queries in
guaranteed polynomial time.Comment: 34 pages, 14 figures, supersedes: http://arxiv.org/abs/1105.281
Nearly Optimal Private Convolution
We study computing the convolution of a private input with a public input
, while satisfying the guarantees of -differential
privacy. Convolution is a fundamental operation, intimately related to Fourier
Transforms. In our setting, the private input may represent a time series of
sensitive events or a histogram of a database of confidential personal
information. Convolution then captures important primitives including linear
filtering, which is an essential tool in time series analysis, and aggregation
queries on projections of the data.
We give a nearly optimal algorithm for computing convolutions while
satisfying -differential privacy. Surprisingly, we follow
the simple strategy of adding independent Laplacian noise to each Fourier
coefficient and bounding the privacy loss using the composition theorem of
Dwork, Rothblum, and Vadhan. We derive a closed form expression for the optimal
noise to add to each Fourier coefficient using convex programming duality. Our
algorithm is very efficient -- it is essentially no more computationally
expensive than a Fast Fourier Transform.
To prove near optimality, we use the recent discrepancy lowerbounds of
Muthukrishnan and Nikolov and derive a spectral lower bound using a
characterization of discrepancy in terms of determinants
On Low Treewidth Approximations of Conjunctive Queries
We recently initiated the study of approximations of conjunctive queries within classes that admit tractable query evaluation (with respect to combined complexity). Those include classes of acyclic, bounded treewidth, or bounded hypertreewidth queries. Such approximations are always guaranteed to exist. However, while for acyclic and bounded hypertreewidth queries we have shown a number of examples of interesting approximations, for queries of bounded treewidth the study had been restricted to queries over graphs, where such approximations usually trivialize. In this note we show that for relations of arity greater than two, the notion of low treewidth approximations is a rich one, as many queries possess them. In fact we look at approximations of queries of maximum possible treewidth by queries of minimum possible treewidth (i.e., one), and show that even in this case the structure of approximations remain rather rich as long as input relations are not binary
Structured learning of metric ensembles with application to person re-identification
Matching individuals across non-overlapping camera networks, known as person
re-identification, is a fundamentally challenging problem due to the large
visual appearance changes caused by variations of viewpoints, lighting, and
occlusion. Approaches in literature can be categoried into two streams: The
first stream is to develop reliable features against realistic conditions by
combining several visual features in a pre-defined way; the second stream is to
learn a metric from training data to ensure strong inter-class differences and
intra-class similarities. However, seeking an optimal combination of visual
features which is generic yet adaptive to different benchmarks is a unsoved
problem, and metric learning models easily get over-fitted due to the scarcity
of training data in person re-identification. In this paper, we propose two
effective structured learning based approaches which explore the adaptive
effects of visual features in recognizing persons in different benchmark data
sets. Our framework is built on the basis of multiple low-level visual features
with an optimal ensemble of their metrics. We formulate two optimization
algorithms, CMCtriplet and CMCstruct, which directly optimize evaluation
measures commonly used in person re-identification, also known as the
Cumulative Matching Characteristic (CMC) curve.Comment: 16 pages. Extended version of "Learning to Rank in Person
Re-Identification With Metric Ensembles", at
http://www.cv-foundation.org/openaccess/content_cvpr_2015/html/Paisitkriangkrai_Learning_to_Rank_2015_CVPR_paper.html.
arXiv admin note: text overlap with arXiv:1503.0154
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